mk chỉ phân tích thôi bạn tự chia nha!
a, \(16x^4-81=(4x^2)^2-9^2=(4x^2-9)(4x^2+9)\)

                    \(=[(2x)^2-3^2](4x^2+9)\)

                    \(=(2x+3)(2x-3)(4x^2+9)\)

b, \(x^3-3x^2+3x-1=(x-1)^3\)

\(x^2-2x+1=(x-1)^2\)

c, \(18x^5+9x^4+3x^3+6x^2+3x+1=(18x^5+9x^4+3x^3)+(6x^2+3x+1)\)

\(=(6x^2+3x+1)(3x^3+1)\)

câu c bạn đánh sai 1 dấu phép toán kìa!!!!

a: \(=\dfrac{2\left(x+2\right)\left(x-1\right)}{x+2}=2x-2\)

b: \(=\dfrac{2x^3+x^2-6x^2-3x+2x+1}{2x+1}=x^2-3x+1\)

c: \(=\dfrac{x^3+2x^2-2x^2-4x+2x+4}{x+2}=x^2-2x+2\)

d: \(=\dfrac{x^2\left(x-3\right)}{x-3}=x^2\)

`@` `\text {Ans}`

`\downarrow`

b)\(\frac{9x^4-6x^3+15x^2+2x+1}{3x^2-2x+5}=\frac{3x^2.\left(3x^2-2x+5\right)+2x+1}{3x^2-2x+5}=3x^2+\frac{2x+1}{3x^2-2x+5}\)

=> đa thức dư trong phép chia là 2x+1

\(\frac{x^3+2x^2-3x+9}{x+3}=\frac{x^3+9x^2+27x+27-7x^2-30x-18}{x+3}=\frac{\left(x+3\right)^3-7x^2-30x-18}{x+3}\)

\(\left(x+3\right)^2-\frac{7x^2+21x+9x+18}{x+3}=\left(x+3\right)^2-\frac{7x.\left(x+3\right)+9.\left(x+3\right)-9}{x+3}\)

\(=\left(x+3\right)^2-\frac{\left(7x+9\right).\left(x+3\right)-9}{x+3}=\left(x+3\right)^2-\left(7x+9\right)-\frac{9}{x+3}\)

=> đa thức dư trong phép chia là 9

p/s: t mới lớp 7_sai sót mong bỏ qua :>

a: =3x^3-15x^2+21x

b: =-x^3+6x^2+5x-4x^2-24x-20

=-x^3+2x^2-19x-20

c: =9x^2+15x-3x-5-7x^2-14

=2x^2+12x-19

d: =10x^2-4x+2/3

Ta có: \(\dfrac{3x^4-8x^3-10x^2+6x-3}{3x^2-2x+1}\)

\(=\dfrac{3x^4-2x^3+x^2-6x^3+4x^2-2x-15x^2+10x-5+2x+2}{3x^2-2x+1}\)

\(=x^2-2x-5+\dfrac{2x+2}{3x^2-2x+1}\)

\(a,=12x^2-4x-6x-2-x-3=12x^2-11x-5\\ b,=12x^2-9x-12x^2-4x+5=5-13x\\ c,=12x^3-4x^2-12x^3-12x^2+7x-3=-16x^2+7x-3\\ d,=\left(x^2-4\right)\left(x^2+4\right)=x^4-16\)

\(=\left(3x^4-3x^3+x^3-x^2+8x^2-8x+9x-9\right):\left(x-1\right)\\ =\left(x-1\right)\left(3x^3+x^2+8x+9\right):\left(x-1\right)\\ =3x^3+x^2+8x+9\)

a: \(=2x^3:\dfrac{-3}{2}x+4x:\dfrac{3}{2}x-5:\dfrac{3}{2}\)

=-4/3x^2+8/3-10/3

=-4/3x^2-2/3

d: \(\dfrac{3x^3-5x+2}{x-3}=\dfrac{3x^3-9x^2+9x^2-27x+22x-66+68}{x-3}\)

\(=3x^2+9x+22+\dfrac{68}{x-3}\)

(6x³-2x²-9x+3):(3x-1)

=[2x²(3x-1)-3(3x-1)]:(3x-1)

=(2x²-3)(3x-1):(3x-1)

=2x²-3

`!`

`(x^3-3x^2):(x-3)`         

`= x^2(x-3)  :(x-3)` 

`=x^2`

`----`

`(2x^2+2x-4):(x+2)`

`=2(x^2+x-2) :(x+2)`

`= 2 (x^2+2x-x-2) :(x+2)`

\(=2\left[x\left(x+2\right)-\left(x+2\right)\right]:\left(x+2\right)\)

`= 2(x+2)(x-1) :(x+2)`

`=2(x-1)`

`-------`

`(x^4-x-14):(x-2)`

https://hoc24.vn/cau-hoi/x4-x-14-x-2-giup-minh.204306769717

bn tham khảo ở đây nha

`----`

`(x^3-3x^2+x-3):(x-3)`

`= x^2(x-3) +(x-3) :(x-3)`

`=(x-3)(x^2+1):(x-3)`

`=x^2+1`